Deformations of free and linear free divisors
نویسندگان
چکیده
منابع مشابه
Linear Free Divisors
A free divisor D in C is linear if its module of logarithmic vector fields has a basis of global vector fields of degree 0. It is then defined by a homogeneous polynomial of degree n and its complement is an open orbit of an algebraic subgroup GD in Gln(C). The best known example is the normal crossing divisor. Many other such divisors arise, for instance, from quiver representations. We give a...
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A complex hypersurface D in Cn is a linear free divisor (LFD) if its module of logarithmic vector elds has a global basis of linear vector elds. We classify all LFDs for n at most 4. By analogy with Grothendieck's comparison theorem, we say that the global logarithmic comparison theorem (GLCT) holds for D if the complex of global logarithmic di erential forms computes the complex cohomology of ...
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We introduce the concept of a prehomogeneous determinant as a possibly nonreduced version of a linear free divisor. Both are special cases of prehomogeneous vector spaces. We show that the roots of the b-function are symmetric about −1 for reductive prehomogeneous determinants and for regular special linear free divisors. For general prehomogeneous determinants, we describe conditions under whi...
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In algebraic geometry, it is rather typical that the embedding of a variety Y in another varietyX forces strong constraints on the existence of free linear series on Y . For example, a classical result in plane curve theory states that the gonality of a smooth plane curve of degree d is d − 1 ([ACGH]). It is then natural to look for general statements of this flavor. One particular case, which ...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2013
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2824